Servo control method

ABSTRACT

The servo control method operates a set value of a first-order lag time constant of a feedback compensation by both a detected mechanical position value and a transfer function corresponding to a change of an angular velocity about each axis under a multiple-axes simultaneous control. Further, the servo control method sets a feedforward amount so that the transfer function about the each axis is the same.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a servo control method to synchronouslycontrol multi axes of machines. Especially, this invention relates tothe servo control method about a Numerical Control machine tool(hereinafter, Numerical Control is abbreviated to NC.), a robot and thelike to control a contour.

2. Description of the Related Art

Recent machine tools have been demanded to drive the machine at a highvelocity or a high acceleration/deceleration in order to improve workingefficiency. Further, a high-precision contouring control is demanded.The contouring control is to relate motions about two axes or moremultiple axes at the same time with a linear interpolation, a circularinterpolation and the like, thereby an aisle of tool is alwayscontrolled.

There are following problems at a high acceleration/decelerationoperation and a high velocity operation.

(1) A ball screw is extended (due to an elastic deformation) by aninfluence of an inertial force caused by the highacceleration/deceleration, whereby generating a distance between acommanded position and a present position.

(2) A radius reduction amount is increased by the high-velocityoperation.

(3) Ordinarily, a table is mounted on a saddle, and then a mass ratiobetween a spindle and a column is twice or more in a vertical typemachine. Also in a horizontal type machine, the mass ratio between thespindle and the column is twice or more if a column drive and the likeare employed. If the two axes are driven at the same time under theabove-described condition, an error due to the inertial force isincreased twice or more, so that an elliptic error is generated in thecircular interpolation.

(4) At high velocity, a viscous friction increases, and then thevelocity cannot be followed in a transient state. Thus, a phase shiftoccurs, thereby causing an error that an axis of a circularinterpolation is inclined.

Following countermeasures and the like against the above problems havebeen taken conventionally.

(1) As for the velocity, a velocity feedforward corrects a velocityfollow-up error. Also as for the acceleration, an accelerationfeedforward improves a follow-up characteristics of the acceleration.

(2) A linear scale detects and corrects a mechanical position error.

As some technologies for correcting a mechanical elastic deformation ina semi-closed loop control type,

(1) a technology for correcting the elastic deflection by the inertialforce of the machine with the acceleration feedforward (Japanese PatentApplication Laid-Open No. H7-78031)

(2) a technology for correcting the elastic deflection by the inertialforce of the machine with the feedforward by estimating a rigidity(Japanese Patent Application Laid-Open No. H4-271290)

(3) a technology for correcting the elastic deflection of the machineconsidering a load weight and a viscous resistance in the semi-closedloop control type (Japanese Patent Application Laid-Open No.2000-172341)

(4) a technology for correcting the elastic deflection of the machinewith feedforward considering the load weight and the viscous resistance(Japanese Patent Application Laid-Open No. H11-184529) have been wellknown.

The countermeasure (1) is taken with the semi-closed loop control type,thereby cannot correcting a lead error of the ball screw, an error dueto a thermal dislocation and the like. Therefore, a high-precision feeddrive cannot be executed. The countermeasure (2) is executed, and thenthe full closed loop control type generates a time lag corresponding toat least a sampling time, thereby causing a follow-up error. Thus, thelead error of the ball screw, the error due to the thermal dislocationand the like cannot be corrected completely. Further, in terms ofstability, a gain is not increased in a largely loaded machine, so thata contouring precision is deteriorated. Moreover, if the countermeasure(2) is carried out under hybrid control type, a time lag correspondingto a hybrid time constant is generated. In this case, the lead error ofthe ball screw, the error due to the thermal dislocation and the likecannot be corrected. Accordingly, in any case, an oblique elliptic erroris generated in the circular interpolation.

In any of the above-described cases, the hybrid control type in which ascale feedback is added to an encoder feedback as a first-order lagelement has not been described.

The elastic deformation of machine is corrected according to theabove-described method in the hybrid control type, and then a differencein the mechanical characteristics is reflected on a transfer function bythe scale feedback. Therefore, the difference in the mechanicalcharacteristics is reflected on the transfer function in interpolationof multiple axes, thereby causing a contouring motion error. As aresult, a motion precision of the machine is deteriorated.

However, the conventional semi-closed loop control type cannot suppressa mechanical error such as the lead error of the ball screw and thethermal dislocation. As a method for suppressing such the mechanicalerror, it is considered that the hybrid control type and full closedloop control type are major in future.

The control system of the hybrid control type will be described withreference to an approximate block diagram shown in FIG. 1.

In FIG. 1, a reference numeral 11 denotes a servomotor system. Areference numeral 12 denotes a mechanical system including a load suchas a feed screw and a table. A reference numeral 13 denotes a low-passfilter. A reference numeral 14 denotes a pre-compensation part. Further,ω_(o) is a position loop gain, ω_(h) is a first-order lag frequency, sis a Laplace transform operator and G_(m)(s) is a transfer function ofthe mechanical system.

The mechanical transfer function G_(m)(s) is described as follows:

G _(m)(s)=s ²+2ζω_(n) ·s+ω _(n) ²

where ζ is a damping ratio and ω_(n) is a proper angular frequency.

A total transfer function G_(h)(s) in this case equals${G_{h}(s)} = \frac{\frac{\omega_{0}}{s}}{1 + {\frac{\omega_{0}}{s}\left\lbrack {{\frac{\omega_{h}}{s + \omega_{h}}\left\{ {{G_{m}(s)} - 1} \right\}} + 1} \right\rbrack}}$

Substituting s=jω into the above equation, a total frequency transferfunction G_(h)(j ω) equals${G_{h}\left( {j\quad \omega} \right)} = \frac{A + {j\quad B}}{C + {j\quad D}}$

where A=ω_(h)ω_(o)ω_(n) ²

B=ω_(o)ω_(n) ²ω

C=ω⁴−{2ζω_(n)(ω_(h)+ω_(o))+ω_(n) ²}ω²+ω_(h)ω_(o)ω_(n) ²

D=−(ω_(h)+ω_(o)+2ζω_(n))ω³+(ω_(h)+ω_(o))ω_(n) ²ω

As a result of the G_(h)(jω), a gain |G_(h)(jω)| is given as follows:${{G_{h}\left( {j\quad \omega} \right)}} = \sqrt{\frac{A^{2} + B^{2}}{C^{2} + D^{2}}}$

and a phase ∠G_(h)(jω) is${{\angle G}_{h}\quad \left( {j\quad \omega} \right)} = {\tan^{- 1}\left( \frac{{AC} + {BD}}{{BC} - {AD}} \right)}$

where the proper angular frequency ω_(n) is defined as$\omega_{n} = \sqrt{\frac{k}{M}}$

and the damping ratio ζ is defined as $\zeta = \frac{c}{2\sqrt{kM}}$

Therefore, the gain G_(h)(jω) and the phase ∠G_(h)(jω) of the hybridcontrol type are functions of a mass M, a spring constant k, a viscousdamping coefficient c, an angular velocity ω, the first-order lagfrequency (hybrid frequency) ω_(h) and the position loop gain ω_(o).

Ordinarily, according to the hybrid control type, the hybrid frequencyω_(h) and the position loop gain ω_(o) are set to have the same value inall the axes, so that no gain shift occurs.

However, in most cases, the mass M, the spring coefficient k, and theviscous damping coefficient c are different between one axis and anotheraxis in the mechanical system. In other words, the elastic dislocationabout each axis differs on each axis and a difference in the mass M, thespring coefficient k and the viscous damping coefficient c generatesshift of the gain and the phase about each axis. Hence, the shift of thegain or that of the phase occurs between the axes, and then a circularinterpolation motion, which executes two-axes synchronous control,induces a path error (the two axes express X axis and Y axis.Hereinafter, two axes are X axis and Y axis.). Therefore, as shown inFIG. 2, a real circle turns to be an oblique ellipse.

X-axis gain and Y-axis gain are exemplified in FIGS. 3A and 3B. X-axisphase and Y-axis phase are exemplified in FIGS. 4A and 4B. In thisexample, a proper frequency of the X axis is low, thereby indicatingthat a peak of gain occurs at a resonance point of the machine and thereis a large different gain in neighborhood of the resonance point. Inaddition, the difference of the phase is also large near the resonancepoint. Therefore, an oblique-elliptical motion locus is generated.

Next, the control system of the full closed loop control type will bedescribed with reference to the approximate block diagram shown in FIG.5.

A mechanical transfer function G_(m)(s) in this case is described asfollows:

G _(m)(s)=s ²+2ζω_(n) ·s+ω _(n) ²

A total transfer function G_(full)(s) in this case equals${G_{full}(s)} = \frac{\frac{\omega_{0}}{s}{G_{m}(s)}}{1 + {\frac{\omega_{0}}{s}{G_{m}(s)}}}$

Substituting s=jω into the above equation, a total frequency transferfunction G_(full)(jω) is${G_{full}\left( {j\quad \omega} \right)} = \frac{A_{f} + {j\quad B_{f}}}{C_{f} + {j\quad D_{f}}}$

where A_(f)=ω_(o)ω_(n) ²

B_(f)=0

C_(f)=−2ζω_(n)ω²+ω_(o)ω_(n) ²

D_(f)=−ω³+ω_(n) ²ω

As a result of the G_(full)(jω), a gain |G_(full)(jω)| is solved asfollows:${{G_{full}\left( {j\quad \omega} \right)}} = \sqrt{\frac{A_{f}^{2} + B_{f}^{2}}{C_{f}^{2} + D_{f}^{2}}}$

and a phases ∠G_(full)(jω) is solved as follows:${{\angle G}_{full}\left( {j\quad \omega} \right)} = {\tan^{- 1}\left( \frac{{A_{f}C_{f}} + {B_{f}D_{f}}}{{B_{f}C_{f}} - {A_{f}D_{f}}} \right)}$

where the proper angular frequency ω_(n) is defined as$\omega_{n} = \sqrt{\frac{k}{M}}$

and the damping ratio ζ is defined as$\zeta = \frac{c}{2\sqrt{k\quad M}}$

Therefore, the gain G_(full)(jω) and the phase ∠G_(full)(jω) of the fullclosed loop control type are functions of the mass M, the springconstant k, the viscous damping coefficient c, the angular velocity ωand the position loop gain ω_(o).

Ordinarily, the position loop gain ω_(o) is set to have the same valuein all the axes, so that no gain shift occurs. However, in most cases,the mass M, the spring coefficient k and the viscous damping coefficientc are different about each axis of the mechanical system.

Accordingly, in case of the full closed loop control type which cancorrect a mechanical error ideally, a lag corresponding to one cycle ofthe position loop occurs. Thus, such differences in these mechanicalfeatures generate a shift of the gain and the phase about each axis.Therefore, the circular interpolation motion about two axes is executedunder the condition that the shift occurs in the gain and the phasebetween the axes. Then, the oblique elliptical motion shown in FIG. 2occurs.

SUMMARY OF THE INVENTION

A first object of the present invention is to provide a servo controlmethod for correcting an elastic dislocation error in hybrid controltype or full closed loop control type including scale feedback, which isfeedback compensation with a detected mechanical position value. Asecond object of the present invention is to provide a servo controlmethod for suppressing a synchronous error in interpolation on multipleaxes. A third object is to provide a servo control method for improvinga contouring motion precision.

The first aspect of the present invention provides a servo controlmethod comprising the steps of: operating both a set value of afirst-order lag time constant of a feedback compensation by a detectedmechanical position value and a transfer function corresponding to achange of an angular velocity for each axis under a multiple-axessimultaneous control; and setting a feedforward amount so that thetransfer function about the each axis is the same.

The second aspect of the present invention provides a servo controlmethod further comprising the steps of: detecting a change amount of aload mass; operating a change amount of an inertial force due to thechange amount of the load mass; and calculating the transfer functionabout the each axis taking the change amount of the inertial force intoaccount.

The third aspect of the present invention provides a servo controlmethod still further comprising the steps of: operating the changeamount of a stiffness about the each axis corresponding to a mechanicalposition of the load mass; and calculating the transfer function aboutthe each axis taking the change amount of the stiffness into account.

The fourth aspect of the present invention provides a servo controlmethod according to the third aspect of the invention, wherein thetransfer function about the each axis is calculated considering both achange of a viscous damping coefficient and a change of a frictionalforce against a feed speed.

The fifth aspect of the present invention provides a servo controlmethod according to the fourth aspect of the invention, wherein athermal dislocation amount difference between the axes is added to anelastic dislocation amount.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an approximate block diagram of hybrid control type;

FIG. 2 shows an explanatory diagram indicating an example of an obliqueelliptical error;

FIGS. 3A and 3B show graphs indicating gain characteristics about twoaxes;

FIGS. 4A and 4B show graphs indicating phase characteristics about twoaxes;

FIG. 5 shows an approximate block diagram of full closed loop controltype;

FIG. 6 shows a block diagram indicating a first embodiment of servocontrol method of the present invention;

FIG. 7 shows a graph indicating the relation between angular velocityand gain ratio between two axes;

FIG. 8 shows a graph indicating measured values about the relationangular velocity and ratio of velocity feedforwards between two axes;

FIG. 9 shows an explanatory diagram indicating a circular interpolationmotion;

FIG. 10 shows a graph indicating the relation between frictional forceand feed speed (comparison of two different kinematic viscosities);

FIG. 11 shows a graph indicating measured values about a difference ofelastic dislocation by inertial force between two axes;

FIG. 12 shows a graph indicating an example of a corrected line whichapproximates the relation between angular velocity and gain ratio; and

FIG. 13 shows a block diagram indicating a second embodiment of servocontrol method of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Hereinafter, the preferred embodiments of the present invention will bedescribed in detail with reference to the accompanying drawings. Inaddition, the embodiments of the present invention are employing thesame reference numerals of the conventional example with the sameconfiguration described above.

FIG. 6 shows an embodiment of the servo control method of the presentinvention. In FIG. 6, a reference numeral 11 denotes a servomotorsystem. A reference numeral 12 denotes a mechanical system includingsuch a load as feed a screw, a table. A reference numeral 13 denoteslow-pass filter. A reference numeral 15 denotes a velocity feedforwardpart. A reference numeral 16 denotes an acceleration feedforward part. Areference numeral 17 denotes an operating part for calculating acorrected value K of the gain ratios between axes. A reference numeral18 denotes a feedforward correcting part.

Information (that is, the angular velocity ω1, the inclination a1, theangular velocity ω2, the inclination a2 and the like) on the ratio oftransfer function about the two axes with position loop gain ω₀,first-order lag frequency ω_(h), acceleration/deceleration time constantT_(a), angular velocity ω is inputted to the operating part 17 as NCparameters. Further, mass M, spring constant k, viscous dampingcoefficient c, ball screw mounting distance L, λ (λ is obtained bymultiplying a ball screw sectional area S by Young's modulus E),frictional force F_(d), frictional torque T_(v) and proper frequency fare inputted as mechanical parameters. The corrected value K of the gainratio between the axes is operated using these NC parameters andmechanical parameters.

The feedforward correcting part 18 corrects both velocity feedforwardK_(v)s and acceleration feedforward K_(a)s² by the corrected value K.

FIG. 7 shows the relation between the angular velocity ω and X-axis gainper Y-axis gain (|G_(x)|/|G_(y)|). FIG. 8 shows the relation between theangular velocity ω and X-axis optimum velocity feedforward per Y-axisoptimum velocity feedforward (FF_(x)/FF_(y)), which is gained as a testresult of an actual machine. It has been confirmed that the relationbetween the ratio of optimum velocity feedforwards (FF_(x)/FF_(y)) andthe angular velocity ω is almost the same as the relation between theratio of gain about two axes (|G_(x)|/|G_(y)|) and the angular velocityω.

Then, the gain ratio about each axis is obtained by the angular velocityω. The gain ratio about each axis is multiplied with feedforward setvalues. Therefore, in case of the hybrid control type, the elasticdislocation can be corrected without generating a path error so as toform an oblique ellipse.

Next, a method for calculating mechanical parameters such as mass M,spring constant k, and viscous damping coefficient c is described. Uponcalculating such mechanical parameters, the semi-closed control methodis employed as a type to control an object machine in which themechanical parameters are calculated.

In the semi-closed loop control type, a transfer function G_(s)(s) froma commanded part to a motor position is given as follows:${G_{s}(s)} = \frac{\omega_{0}}{s + \omega_{0}}$

Absolute value of the above equation is obtained as follows:$\left| {G_{s}({j\omega})} \right| = \frac{\omega_{0}}{\sqrt{\omega_{0}^{2} + \omega^{2}}}$

This equation is a function of ω_(o), so that the transfer function inthe semi-closed loop control type receives no mechanical influence.

Here, a case of a X-Y axes plane is described as an example. Thecircular interpolation motion about both the X axis and the Y axis iscommanded with two turns or more. At this time, a commanded value (thatis, a position calculated from a rotation angle of the servomotor) and amechanical position are detected. Moreover, the pre-compensation is setin order to eliminate an influence of a reduction amount of the radius.

In FIG. 9, commanded values x* and y* about the axes X and Y are definedas

x*=Rcosωt

y*=Rsinωt

where R is a radius of a circle, ω is an angular velocity and t is atime.

The commanded velocities v_(x) about X axis, v_(y) about Y axis and thecommanded accelerations α_(x) about X axis, α_(y) about Y axis aredetermined by the first-order differential of both x* and y* and thesecond-order differential of both x* and y*, respectively, so that belowequations are obtained.

v_(x)=−Rωsinωt

v_(y)=Rωcosωt

α_(x)=−Rω²cosωt

α_(y =−Rω) ²sinωt

If the elastic dislocation σ is calculated from the equation of motion,then $\sigma = {- \frac{{M\quad \alpha} + {c\quad v}}{k}}$

When ω_(t)=2nπ(n is integer, where the motion start point and the motiontermination point are excluded because they may be affected by others).

v_(x)=0

v_(y)=Rω

α_(x)=−Rω²

α_(y)=0

Thus, $\sigma_{x} = \frac{M_{x}R\quad \omega^{2}}{k_{x}}$$\sigma_{y} = {- \frac{c_{y}R\quad \omega}{k_{y}}}$

The elastic dislocation can be measured actually as a difference betweena motor position and a mechanical position. The mass M can be calculatedfrom a design value or a torque. The circle radius R and angularvelocity ω can be read from a program.

Therefore, the stiffness k_(x) about the X axis is determined asfollows: $k_{x} = \frac{M_{x}R\quad \omega^{2}}{\sigma_{x}}$

In addition, when ω_(t)=π/2,

v_(x)=−Rω

v_(y)=0

α_(x)=0

α_(y)=−Rω²

Thus,$\sigma_{x}^{\prime} = \frac{c_{x}R\quad \omega}{k_{x}^{\prime}}$$\sigma_{y}^{\prime} = \frac{M_{y}R\quad \omega^{2}}{k_{y}^{\prime}}$

Therefore, the stiffness k′_(y) about Y axis is determined as follows:$k_{y}^{\prime} = \frac{M_{y}R\quad \omega^{2}}{\sigma_{y}^{\prime}}$

The circle radius R is small, and then it can be considered thatk_(x)=k′_(x) and k_(y)=k′_(y).

Therefore, the viscous damping coefficients c_(x) and c_(y) aredetermined.$c_{x} = {\frac{k_{x}^{\prime}\sigma_{x}^{\prime}}{R\quad \omega} = {M_{x}\omega \frac{\sigma_{x}^{\prime}}{\sigma_{x}}}}$$c_{y} = {{- \frac{k_{y}\sigma_{y}}{R\quad \omega}} = {{- M_{y}}\omega \frac{\sigma_{y}}{\sigma_{y}^{\prime}}}}$

The machine is operated by the circular interpolation under thesemi-closed loop control type, and a position calculated from theservomotor is compared with a mechanical position, thereby the methodfor obtaining both the stiffness and the viscous damping coefficientabout each axis is described above.

Additionally, the axial stiffness, the frictional force and the viscousdamping coefficient can be obtained by an actual measurement of the lostmotion, a static rigidity test, a measurement of the frictional forceand the like.

The above-described calculations are carried out assuming that the axialdirection stiffness k is not changed by the mechanical position underthe condition k_(x)=k′_(x) and k_(y)=k′_(y). However, if ball screwdrive and the like are employed, the axial direction stiffness of thescrew axis is different depending on a position (that is, the mechanicalposition) to which a load is applied.

Even under the condition that he ball screw drive is employed and theaxial stiffness of the screw axis is different depending upon a positionto which the load is applied, the mechanical parameters can be operatedby the above-described actual measurement if the start position of thecircular interpolation is changed. However, the number of measurementsis increased if the above method is employed. The stiffness of the ballscrew axis is determined as a function of a load application positionand the change of the stiffness according to the load applicationposition is operated in advance, thereby an almost strict solution canminimize the number of measurements.

In case of the ball screw drive, the axial direction synthetic stiffnessk equals $k = \frac{k_{T}k_{b}}{k_{T} + k_{b}}$

where k_(b) is the ball screw stiffness and k_(T) is the other syntheticstiffness.

In case where the ball screw is mounted such that both ends thereof arefixed, the ball screw stiffness k_(b) is$k_{b} = {\lambda \frac{L}{l\quad \left( {L - 1} \right)}}$

where λ=S·E (S is ball screw sectional area and E is Young's modulus(Young's modulus is constant.).);

L is a ball screw mounting distance; and

l is a load application position.

The other synthetic stiffness k_(T) includes the stiffness of a ballscrew nut, the stiffness of a ball screw supporting bearing, thestiffness of a nut and a bearing mounting part and the like. If thecircle radius is large, a corrected stiffness k is used in calculatingthe viscous damping coefficient.

In the above description, the viscous damping coefficient c is almostconstant. However, in case that the frictional force varies according tothe sliding speed along Stribeck curve e.g., a sliding guide, and thatthe kinematic viscosity of the lubricant is high and the frictionalforce is not proportional to the sliding speed, the relation between thefeed speed and the frictional force is measured actually. Thus, therelation between the viscous damping coefficient and the feed speed isobtained. In addition, Coulomb friction is compensated by thefeedforward control of the torque by means that correcting the quadrantstub at the time of an axis inversion.

FIG. 10 shows an example of the relation between the feed speed and thefrictional taking the amount of the kinematic viscosity into account.

The following method is available as an example of the method formeasuring the relation between the feed speed and the frictional force.Namely, there is a method that the feed axis torque under a steady state(the machine is not accelerated under this state.) at the time of theone-axis linear interpolation is detected and recorded every each feedspeed. In this method, a memory for recording the frictional force dataversus the feed speed data is only needed.

Using the above-described method, the viscous damping coefficient c₀under a certain condition is obtained. The viscous damping coefficientc_(n) against an arbitrary feed speed can be determined as follows:$c_{n} = {\frac{T\quad v_{n}}{T\quad v_{0}}c_{0}}$

where Tv_(n) and Tv₀ are the frictional torque against the arbitraryfeed speed.

In case of the ball screw drive, the relation between a frictionaltorque T and a frictional force F_(d) is described as follows:$T = {\frac{P}{2\pi}F_{d}}$

where P is a lead of ball screw and F_(d) is a rate of the torque changeaccompanied with the feed speed change. F_(d) corresponds to a rate ofthe frictional force change.

Further, a change amount of motional mass is detected, such that achange amount of the inertial force can be operated and corrected. Amethod for detecting the change amount of the motional mass isdescribed. Before and after a load mass is mounted on a work table, theone-axis linear interpolation under the same feed speed condition iscommanded, so as to measure the torque under the steady state. Inertialmoment is approximated by an increase amount of the torque under thesteady state, so that the load mass can be estimated.

In the case that the proper frequency in the axial direction of themachine can be detected (e.g., a case that the open loop transferfunction of the velocity control can be obtained), the change of themass can be determined from the change of the proper frequency.

The proper frequency f is defined as$f = {\frac{1}{2\pi}\sqrt{\frac{k}{M}}}$

Therefore, $M = \frac{k}{\left( {2\pi \quad f} \right)^{2}}$

Accordingly, the change of the mass is inversely proportional to thesquare of the change of the proper frequency.

Next, a method for measuring a difference between the elasticdislocations about two axes according to the inertial force isdescribed. Here, one example (namely, the difference of the elasticdislocations about two axes is measured actually.) will be described,the linear interpolation motion about two axes at 45° is commanded, andthen an error Δσ(=σ_(x)−σ_(y)) at a time of the acceleration or thedeceleration is detected. FIG. 11 shows an example of the result of theactual measurement. Moreover, FIG. 11 shows a difference between X-axiselastic dislocation and Y-axis elastic dislocation being generated bythe inertial force.

If the frictional forces are almost the same about X axis as about Yaxis, the elastic dislocation about X axis and the elastic dislocationabout Y axis are obtained as follows:$\sigma_{x} = \frac{M_{x}\alpha}{k_{x}}$$\sigma_{y} = \frac{M_{y}\alpha}{k_{y}}$

The mass is known preliminarily, and then the stiffness about each axiscan be calculated by measuring the acceleration under two or moreconditions as shown above.

In some cases, Abbe's error may exist in a position detector (a scaleand the like) provided on the machine, or the deflection of the machinestructure may be included. In the case that Abbe's error exists, themechanical position is not detected with any scale, but theabove-described circular interpolation precision is measured with aplane scale about two axes. Then, the mechanical position is comparedwith the commanded position value. If the deflection of the machinestructure is so large, it may be measured at plural points, therebyobtaining the relation between the measurement point and the deflectionof the machine structure at the measurement point. Further, thedeflection of the machine structure may be calculated by the structuralanalysis (e.g., finite element method) in advance, so as to correct thecalculated value of the deflection of the machine structure.

Next, a method for correcting the difference between the transferfunctions about two axes will be described. FIG. 7 shows the relationbetween the angular velocity ω and X-axis gain per Y-axis gain(|G_(x)|/|G_(y)|). However, it needs labor very much to strictly solvethe ratio of the transfer functions about two axes. It may be adoptedthe approximation based on a curve as shown in FIG. 7.

EXAMPLE 1

The hybrid transfer function includes the first-order lag element. Thus,the approximation is done with the exponential function.

EXAMPLE 2

If the angular velocity is low, the gain shift is small. Then, the valueof the X-axis gain per Y-axis gain can be regarded to be almost 1. Thus,(1) this correction coefficient of the value of the X-axis gain perY-axis gain is assumed to be 1 up to a certain angular velocity. (2) Atthe angular velocity range greater or equal to the angular velocity ωaat which the value of the X-axis gain per Y-axis gain is so large, acurve at the foregoing angular velocity range is linearly approximatedwith plural straight lines.

FIG. 12 shows a correcting pattern of the example 2. In FIG. 12, a fullline expresses a strict solution and a dotted line expresses a correctedline. FIG. 12 is an example in which the approximation is done withthree straight lines. Straight line 1 is characterized by that anangular velocity ω1 equals 18 and an inclination of the straight line 1a1 equals 0. Straight line 2 is characterized by that an angularvelocity ω2 equals 45 and an inclination of the straight line 2 a2equals 0.0009. Straight line 3 is characterized by that an angularvelocity ω3 is infinity and an inclination of the straight line 3 a3equals 0.0002. Therefore, the above-described correcting patternsimplifies complicated operations, so that the number of NC operationalprocessing can be decreased.

FIG. 13 shows an embodiment of the servo control method of the presentinvention in which the viscous friction varies due to the machinecondition. In FIG. 13, like a reference numerals are attached to thesame components as FIG. 6 and description thereof is omitted.

NC parameters and mechanical parameters are inputted to a correctedvalues operating part 17 like the above-described embodiment, so that avelocity feedforward corrected coefficient K1 and an accelerationfeedforward corrected coefficient K2 are operated in the correctedvalues operating part 17.

A velocity feedforward correcting part 19 corrects a velocityfeedforward K_(v)s with the corrected coefficient K1. An accelerationfeedforward correcting part 20 corrects an acceleration feedforwardK_(a)s² with the corrected coefficient K2.

Therefore, In the case that the viscous friction varies due to themachine condition, the velocity feedforward K_(v)s and the accelerationfeedforward K_(a)s² can be corrected with the independent correctedcoefficients K1 and K2.

In any embodiment, a heat change correction can be done about an axis inwhich the heat conduction about the axis is very different from the heatconduction about other axes. The heat change correction is to multiply athermal corrected coefficient with a frictional force and adding adifference of a thermal dislocation amount between the axes is added toan elastic dislocation amount

Moreover, the servo control method of the present invention can beapplied to the full closed loop control type as well as the hybridcontrol type.

According to the servo control method of the present invention, thisservo control method is carried out to multiple axes using the hybridcontrol type or the full closed loop control type, and then the gainshift, which is generated by a mechanical characteristics differenceabout each axis, can be corrected. Further, a contouring motion errorcan be reduced. In addition, this servo control method particularlyeffectuates the reduction of an oblique elliptic error at a high-speedcircular interpolation or at an orbit boring and effectuates thereduction of the contouring motion error in transient state.

The present disclosure relates to subject matter contained in JapanesePatent Application No. 2001-121239, filed on Apr. 19, 2001, thedisclosure of which is expressly incorporated herein by reference in itsentirety.

While the preferred embodiments of the present invention have beendescribed using specific terms, such description is for illustrativepurposes. It is to be understood that the invention is not limited tothe preferred embodiments or constructions. To the contrary, theinvention is intended to cover various modifications and equivalentarrangements. In addition, while the various elements of the preferredembodiments are shown in various combinations and configurations, whichare exemplary, other combinations and configurations, including more,less or only a single element, are also within the spirit and scope ofthe invention as defined in the following claims.

What is claimed is:
 1. A servo control method comprising the steps of:operating both a set value of a first-order lag time constant of afeedback compensation by a detected mechanical position value and atransfer function corresponding to a change of an angular velocity foreach axis under a multiple-axes simultaneous control; and setting afeedforward amount so that the transfer function about the each axis isthe same.
 2. A servo control method according to claim 1, furthercomprising the steps of: detecting a change amount of a load mass;operating a change amount of an inertial force due to the change amountof the load mass; and calculating the transfer function about the eachaxis taking the change amount of the inertial force into account.
 3. Aservo control method according to claim 2, still further comprising thesteps of: operating the change amount of a stiffness about the each axiscorresponding to a mechanical position of the load mass; and calculatingthe transfer function about the each axis taking the change amount ofthe stiffness into account.
 4. A servo control method according to claim3, wherein the transfer function about the each axis is calculatedconsidering both a change of a viscous damping coefficient and a changeof a frictional force against a feed speed.
 5. A servo control methodaccording to claim 4, wherein a difference of a thermal dislocationamount between the axes is added to an elastic dislocation amount.